Galaxy Note 3 Wifi Connection Is Unstable Solved

Just Install this apps from play store my problem solved.

https://play.google.com/store/apps/details?id=com.farproc.wifi.statIc&hl=en

WiFi Static Description :

Manages your Wi-Fi static IP configurations and even switches automatically!

You can set static IP with the built-in Settings app(Wireless & networks, Wi-Fi
settings, menu key, Advanced), but it maintains only ONE
configuration. This app is an enhancement of that.

After Install that apps Go to the apps then choose Add Configuration..

Fill the DNS1 with your IP address (my router IP is 192.168.1.1 maybe different with your IP router)

DNS 2 with google DNS (8.8.8.8)  or your best DNS in your country.

then restart your modem and forget your Wifi from Wifi setting..

after that Connect your device to the Wifi network...

I hope that apps can solve your problem 

:)